Question

parabolao find appropriate values of a, h, and k using the given information:  The arch is 290 feet high.  The arch is 275 feet wide at ground level.  The function you find should assume that the arch is place in a coordinate system in which the x axis is at ground level and the y axis goes through the left hand side at ground level (see below).

Answer 1

The appropriate values of a, h, and k are -1. 137.5 and 145, respectively

How to determine the appropriate values of a, h, and k

From the question, we have the following parameters that can be used in our computation:

Height = 290 ft

Width = 275 ft

The value of h and k is the vertex of the parabola

This is represented as

Vertex = (h, k)

These values are the midpoints of the height and the width

So, we have

h = 275/2

h = 137.5

For k, we have

k = 290/2

k = 145

A parabola is represented as

y = a(x - h)² + k

So, we have

y = a(x - 137.5)² + 145

Because it is an arch

Then the leading coefficient is negative

In this case, we set a to -1

Hence, the appropriate values of a, h, and k are -1. 137.5 and 145